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A Star-Variety With Almost Polynomial Growth☆

The representation theory of the symmetric group is used to study varieties of linear algebras over a field of characteristic 0. The relatively free algebras and the lattice of subvarieties of the variety of Lie algebras are described. An example of an almost finitely based variety of linear algebras if constructed. A continuous set of locally finite varieties forming a chain with respect to inclusion is indicated. Information is obtained on the variety of Lie algebras (resp., associative algebras with 1) generated by the second-order matrix algebra. In particular, distributivity of the lattice of subvarieties is proved, and in the Lie case a relatively free algebra is described.Bibliography: 16 titles.

Representations of the symmetric group and varieties of linear algebras

INTRODUCTION
Digital morphology analyzers are increasingly replacing light microscopy in laboratory hematology practice. This study aimed to perform the analytical validation of the white blood cell (WBC) differential and of reliability of platelet assessment on Sysmex DI-60 (Kobe, Japan).


METHODS
Validation included determination of within-run and between-run precision for WBC differential according to the CLSI EP15-A3 protocol, accuracy and method comparison with light microscopy and with the automated WBC differential from the Sysmex XN-10 hematology analyzer, reliability of platelet clump detection and platelet count estimation.


RESULTS
Standard deviations of both pre- and post-classification mostly satisfied manufacturer's criteria for imprecision. Accuracy assessment revealed that only eosinophil count (1.4%) in one peripheral blood smear (PBS) remained outside the declared range (2-10%) after reclassification. Method comparison between DI-60 and light microscopy yielded Spearman's correlation coefficients from 0.37 (basophils) to 0.94 (neutrophils and lymphocytes), minor proportional difference for bands, constant difference for monocytes, both constant and proportional difference for lymphocytes and statistically significant biases for bands, lymphocytes, monocytes and basophils. Diagnostic sensitivity (Se) and specificity (Sp) of DI-60 in detecting immature/pathological cells were 88.7% (95%CI:81.1-94.0) and 83.0% (95%CI:78.7-86.7), respectively, with the area under the curve (AUC) of 0.86 (95%CI:0.82-0.89). Agreement in detection of platelet clumps was 94.8% (kappa coefficient = 0.67, 95%CI:0.53-0.80). Se and Sp of DI-60 to detect platelet clumps were 65.7% (95%CI: 47.8-80.9) and 96.9% (95%CI: 93.9-98.6), respectively, while AUC was 0.81 (95%CI: 0.76-0.86).


CONCLUSION
DI-60 provides reliable WBC differential and platelet assessment. In doubtful cases, the use of light microscopy is still mandatory.

Analytical validation of white blood cell differential and platelet assessment on the Sysmex DI-60 digital morphology analyzer.

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Representations of the symmetric group and varieties of linear algebras

Analytical validation of white blood cell differential and platelet assessment on the Sysmex DI-60 digital morphology analyzer.